Yes they are.
I disagree. Even if they ultimately come from a common ancestor, in order to classify two characteristics as homologous, they have to have some similarities. After millions of years of being in the oceans, the fins of whales have evolved such that they are not at all similar to cats' legs.
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Penguin flippers and bat wings have evolved independently from one another. If it was another bird with the penguin, their wings would be homologous traits since all birds have wings, but not all mammals have wings. Therefore these two traits are analogous since they are similar to one another but bat wings evolved independently.
Yes, they are.
One sense of the word homologous pertains to organs (or appendages): Similar in position, structure, and evolutionary origin but not necessarily in function; for example, a seal's flipper is homologous with the human arm.
They are homologous structures mostly because of its fins, they look like only one bone but is actually a structure of a hand inside